Answer:
1. ∠A = 71.9°
2. ∠B = 62.9°
3. ∠C = 27.5°
Step-by-step explanation:
By using a calculator, we have;
cos A = 0.31
sin B = 0.89
tan C = 0.52
1. Therefore, ∠A = cos⁻¹(0.31), inputting the digits in the calculator and looking for the inverse sign, we have;
∠A = cos⁻¹(0.31) = 71.94° = 71.9° to the nearest tenth of a degree.
2. For sin B = 0.89, we have;
∠B = sin⁻¹0.89 = 62.873° ≈ 62.9° with the answer rounded to the nearest tenth of a degree.
3. Similarly, for tan C = 0.52, inputting the values in the calculator and pressing the tan⁻¹ button, we have;
∠C = tan⁻¹(0.52) = 27.474°, which is 27.5° rounded to the nearest tenth of a degree.
The watch Bea would like to buy costs $10 less than 2
times the amount she has saved. The watch costs $50.
How much money does Bea have saved?
Could whoever answers pls tell the equation used?
Answer: Bea has $30 saved
Step-by-step explanation:
Add 10: 50+10=60
Divide by 2: 60/2=30
A town's population is 53 comma 350. About 75 people move out of the town each month. Each month, 175 people on average move into town. A nearby town has a population of 55 comma 825. It has no one moving in and an average of 175 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.
Answer:
In about 9 months the population of the towns will be equal.
Step-by-step explanation:
The population of both cities, after t months, can be modeled by linear functions.
Town A:
Population of 53330.
About 75 people move out of the town each month. Each month, 175 people on average move into town.
So, after t months, the population will be:
[tex]A(t) = 53300 + (175 - 75)t[/tex]
[tex]A(t) = 53300 + 100t[/tex]
Town B:
Population of 55,825.
An average of 175 people moving away every month.
So, after t months, the population will be:
[tex]B(t) = 55825 - 175t[/tex]
In about how many months will the populations of the towns be equal?
This is t for which:
[tex]A(t) = B(t)[/tex]
[tex]53300 + 100t = 55825 - 175t[/tex]
[tex]275t = 2525[/tex]
[tex]t = \frac{2525}{275}[/tex]
[tex]t = 9.18[/tex]
Rounding to the nearest number
In about 9 months the population of the towns will be equal.
According to the latest survey the mean world lifespan is 68.8 years the university of Oregon wants to see if the average life span of the residence of Oregon differs from the world average suppose a study followed a random sample of 26 Oregonians and found their average lifespan to be 72.8 years with a standard deviation of 2.5 years
Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
µ = 68.8
For the alternative hypothesis,
µ ≠ 68.8
This is a two tailed test.
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 26,
Degrees of freedom, df = n - 1 = 26 - 1 = 25
t = (x - µ)/(s/√n)
Where
x = sample mean = 72.8
µ = population mean = 68.8
s = samples standard deviation = 2.5
t = (72.8 - 68.8)/(2.5/√26) = 8.16
We would determine the p value using the t test calculator. It becomes
p < 0.00001
Assuming a significance level of 0.05, then
Since alpha, 0.05 > than the p value, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the average life span of the residence of Oregon differs from the world average.
what is 24% of 135??
Answer:
32.4
135 x 24% = 135 x 0.24 = 32.4
Step-by-step explanation:
Answer:
32.4
Step-by-step explanation:
135 times 24 dived by 100
In the past twenty years, scientists have seen the sea level rise at a rate of approximately 0.13 inches per year. If this rate continues, which best represents the change in sea level over the next 27 months (2.25 years)?
Answer:
The change in the sea level will be by 0.2925 inches
Step-by-step explanation:
First of all , we will need to write out the rate at which the sea level is rising. This is 0.13 inches, per year. This means that every year, the sea level increases by 0.13 inches.
Since the sea level increases by 0.13 inches every year, in 2.25 years, to get the sea level, we will have to multiply the current rate at which it is rising by that duration of time.
This will be 2.25 years X 0.13 inches/ year = 0.2925 inches
Therefore, the change in the sea level will be by 0.2925 inches
Answer:
0.2925 inches
Step-by-step explanation:
Need help pls have no idea how to this
Answer:
The local minimum point of f(x) is at the point (-2,-2)
Step-by-step explanation:
the minimum point is located on the very bottom of the parabola!
so its cut off but its (-2,-2)
sorry I didnt see the 6,-2
so I am gussing the y-value is the minimum point so it should be -2....tell me if I am wrong but if your looking for a points it (-2,-2) if your looking for the value it would be -2
pls mark me brainliest
The graph of a polynomial is shown below. Is its highest power even or odd? Explain.
Answer:
Step-by-step explanation:
the graph is at the highest power at the top left corner because the graph shape has a even or odd chance so that is the answer
It's highest power is odd
What is graph of polynomial ?
The graph of a polynomial function will touch the x-axis at zeros with even multiplicities. The graph will cross the x-axis at zeros with odd multiplicities. The sum of the multiplicities is the degree of the polynomial function.
According to the question,
Graph of polynomial is shown in given graph,
(1) at point A graph passes linearly
(2) At point b, graph passes x-axis cubically
(3) At point c, Graph passes x-axis linearly
Hence, polynomial having degree 5
Hence, it's highest power is odd
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I need help ASAP. All the help I can get it appreciated
Answer:
QRU and VUR
Step-by-step explanation:
Alternative interior angles are angles that have the same degrees, but different locations. In this case, you can see QRU has the same degree of angle as VUR; They are only in different locations.
- Hope that helps! Please let me know if you need further explanation.
Answer:
QRU and VUR
Step-by-step explanation:
Hope this helps!
The key for a stem and leaf plot is 3|4. which number is the stem? which number is the leaf?
Answer:
The number 3 is the stem.
The number 4 is the leaf.
Step-by-step explanation:
The Stem and Leaf Plot is a mathematical table used for the graphical representation of a data set. It involves splitting each data value into a stem (typically the first number, on the left) and a leaf (the last number, on the right).
The stem list is used for grouping data value downwards while the leaf values move rightward from its respective stem values and it's used for showing each data value within a group.
Also, the key of a stem and leaf plot is used as a guide on how to read the data set.
For example, the key for a stem and leaf plot is 3|4. Thus, the number 3 is the "stem" and the number 4 is the "leaf."
help me pls i dont know what to do
The answer is the last one: k = 5
Hope I helped and good luck!
Graph x^3 + 3x^2 − x − 3 = 0. What are the solutions to the equation?
x = −3, x = 0, and x = 1
x = −3, x = −1, and x = 0
x = −3, x = −1, and x = 1
x = −1, x = 1, and x = 3
Answer:
x = −1, x = 1, and x = - 3
Step-by-step explanation:
hello :
if : x=1 1^3 + 3×1^2 − 1 − 3 =1+3-1-3 =4-4=0......true
if : x=-1 (-1)^3 + 3×(-1)^2 +1− 3 =-1+3.+1-3.=0...true
if : x=3 (-3)^3 + 3×(-3)^2 + 3 − 3 =-27+27+3-3.=0.....true
Humberto deposited $50 in a new account at his bank. The bank pays 5.3% annual simple interest on this account. Humberto makes no additional deposits or withdrawals. How much money will be in his account at the end of 5.5 years?
Answer:
$58.415
Step-by-step explanation:
Initial value: 50 dollars
Independent variable: 5.3%
Dependent variable: Y
This equation can be written in slope intercept form:
[tex]y=mx+b[/tex]
[tex]y= 1.53x+50[/tex]
x= the number of years
[tex]y= 1.53(5.5)+50[/tex]
[tex]y=8.415+ 50[/tex]
[tex]y= 58.415[/tex]
You have a 10 gallon jug and a 3 gallon jug. Both jugs are unmarked. You need exactly 5 gallons of water. How can you get it if a water faucet is available?
Answer:
Step-by-step explanation:
You have a 10 gallon jug and a 3 gallon jug and need exactly 5 gallons of water.
This what you do:
- Fill the 3 gallons jug full and pour into the 10 gallons keg
- Repeat the above a second time making a total of 6 gallons of water in the 10 gallons jug.
- Fill the 3 gallons jug a third time and pour into the 10 gallons jug making 9 gallons
- Fill the 3 gallons jug the fourth time and pour into the 10 gallons jug till full leaving 2 gallons of water remaining in the 3 gallons jug.
- Then empty out the 10 gallons jug and pour the 2 gallons of water in the 3 gallons jug into the 10 gallons jug.
- Then, fill the 3 gallons jug again and pour into the 10 gallons jug holding the 2 gallons of water making a total of 5 gallons of water in the 10 gallons jug.
Hope, that helps!!!
Thanks for all the help
Answer:
<FBE
Step-by-step explanation:
supplementary just mean 180
Answer:
∠CBG or ∠FBG
Step-by-step explanation:
Supplementary angles add up to 180°.
Sarah and Gabriela are at a soccer camp. The length of a soccer practice is 2/3 hour. The coaches have set aside 8 hours for soccer practice. How many soccer practices can the coaches have?
Answer:
12 soccer practices
Step-by-step explanation:
1 Soccer practice = 2 / 3 hour
We have 8 hours
8 / 2/3
multiply the top and bottom by 3 to get rid of the 3
8 * 3 = 24
2/3 * 3 = 2
24 / 2 = 12
Answer:
One way to answer your problem is by using proportions, and the following method can be done:
Step-by-step explanation:
[tex]\frac{1}{\frac{2}{3}}=\frac{x}{8}[/tex]
Then that reduces to the following:
[tex]\frac{8}{\frac{2}{3}}=x=12[/tex]
So the answer would be 12 practices.
Paint costs $12 per litre and can only be purchased in a full number of litres. One litre of paint covers an area of 10m2. A rectangular wall is 6.5 long and 3m high and needs two coats of paint. What will be the cost of paint for the wall?
Answer:
$48
Step-by-step explanation:
The rectangular wall is 6.5 m long and 3 m high and needs two coats of paint. This means the wall will be painted twice.
First, we find the area of the wall. The area of a rectangle is given as:
A = L * B
where L = length and B = breadth
Therefore, the area of the wall is:
[tex]A = 6.5 * 3 = 19.5 m^2[/tex]
One litre of paint covers an area of [tex]10m^2[/tex].
The paint can only be purchased in a full number of litres.
Therefore, let us find how many litres it will take to paint the wall once:
[tex]10m^2[/tex] = 1 litre
[tex]19.5 m^2[/tex] = 19.5 / 10 = 1.95 litres
Since the paint can only be bought in full number of litres, we approximate 1.95 litres to whole number, that is 2 litres.
2 litres is needed to paint the wall once.
Therefore, we need double of that to paint the wall twice, that is:
2 * 2 = 4 litres
Paint costs $12 per litre, therefore, the price for 4 litres is:
4 * 12 = $48
The cost of paint for the wall is $48.
The mean weight of females in a class is 60kg and that of the males is 72kg. If the mean
weight of the class is 68kg, what is the ratio of females to males in the class?
Answer:
1:2
Step-by-step explanation:
Let's say there are x males and y females in the class.
The sum of all male weights will be 72x, and the sum of all female weights will be 60y.
If we get a class mean weight, we have:
(72x + 60y) / (x+y) = 68
72x + 60y = 68x + 68y
4x = 8y
y / x = 4/8 = 1/2
So the ratio of females to males is the class is 1:2
set x is the set of all multiples of 6 between 15 and 70 what set is equal to set x
Answer:
X ∈ { 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 206, 312, 318, 324, 330, 336, 342, 348, 354, 360, 366, 372, 378, 384, 390, 396, 402, 408, 414 }
Step-by-step explanation:
See procedure below;
Set X { all multiples of 6 between 15 and 70, provided multiples belong to the set of natural numbers },
Set X { 6n | 15 < n < 70, n ∈ natural numbers },
n ∈ { 16, 17, 18, 19, 20, 21, 22, 23, 24, 25.........69 },
X ∈ { 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156.........414 }
Answer; { 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 206, 312, 318, 324, 330, 336, 342, 348, 354, 360, 366, 372, 378, 384, 390, 396, 402, 408, 414 }
The data of set A is A = {18, 24, 30, 36, 42, 48, 54, 60, 66}
What is union and intersection of sets?The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the set be represented as A
Now , the value of A is
A = set of all multiples of 6 between 15 and 70
On simplifying , we get
A = {18, 24, 30, 36, 42, 48, 54, 60, 66}
Hence , the set is A = {18, 24, 30, 36, 42, 48, 54, 60, 66}
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can i get the answer ASAP
Answer:
Step-by-step explanation:
If two triangles are similar, the ratio of the area of the triangles is proportional to the squares of its corresponding sides.
area of ΔJKL/area of ΔLMN = (JK)²/(NM)²
[tex]\frac{392}{8}=\frac{(35)^{2}}{(NM)^{2}}\\\\49=\frac{(35)^{2}}{(NM)^{2}}\\[/tex]
Cross multiply,
49*(NM)²= 1225
[tex](NM)^{2}=\frac{1225}{49}\\\\(NM)^{2}=25\\\\NM=\sqrt{25}\\\\[/tex]
NM = 5 cm
WILL MARK BRAINIEST!!!
What is the solution to the system of equations?
(−1, 3)
(1, −3)
(1, 3)
(−1, −3)
Answer:
(1,-3)
Step-by-step explanation:
Find the 90th term of the arithmetic sequence 16 , 21 , 26
Answer:
The 90th term of the arithmetic sequence is 461.
Step-by-step explanation:
Arithmetic sequences concepts:
The general rule of an arithmetic sequence is the following:
[tex]a_{n+1} = a_{n} + d[/tex]
In which d is the common diference between each term.
We can expand the general equation to find the nth term from the first, by the following equation:
[tex]a_{n} = a_{1} + (n-1)*d[/tex]
In this question:
[tex]a_{1} = 16, d = 21 - 16 = 26 - 21 = 5[/tex]
So
90th term
[tex]a_{90} = a_{1} + (90-1)*d[/tex]
[tex]a_{90} = 16 + 89*5[/tex]
[tex]a_{90} = 461[/tex]
The 90th term of the arithmetic sequence is 461.
Write the equation of a line that passes through the point (6,-3) and has a slope of -2
A. y= -2x+9
B. y= -3x+6
C. y= 6x-3
D. y=9x-2
Answer:
A
Step-by-step explanation:
You don't have to do anything, the only equation with a slope of -2 is A.
Please help me, I’m sort of stuck
Answer: 297 fr squared
Step-by-step explanation:
A data set has a lower quartile of 3 and an interquartile range of 5. Which box plot could represent this data set?
A box-and-whisker plot. The number line goes from 0 to 25. The whiskers range from 2 to 15, and the box ranges from 3 to 8. A line divides the box at 6.
A box-and-whisker plot. The number line goes from 0 to 25. The whiskers range from 4 to 16, and the box ranges from 4 to 11. A line divides the box at 9.
A box-and-whisker plot. The number line goes from 0 to 25. The whiskers range from 2 to 15, and the box ranges from 3 to 10. A line divides the box at 8.
A box-and-whisker plot. The number line goes from 0 to 25. The whiskers range from 3 to 16, and the box ranges from 4 to 9. A line divides the box at 7.
Answer:A
Step-by-step explanation:
A box-and-whisker plot. The number line goes from 0 to 25. The whiskers range from 2 to 15, and the box ranges from 3 to 8. A line divides the box at 6. Option A is correct.
What is a box plot?A straightforward method of expressing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, with a vertical line inside to indicate the median value. Horizontal lines on both sides of the rectangle show the lower and upper quartiles.
Here,
The lower quartile (Q1) of the data set is 3, so the bottom of the box must start at 3.
The interquartile range (IQR) is 5, so the upper quartile (Q3) must be
Q1 + IQR = 3 + 5 = 8
The median (also called the first quartile) is halfway between Q1 and Q3, so it must be at (Q1 + Q3) / 2 = (3 + 8) / 2 = 6.
The whiskers extend to the minimum and maximum values within 1.5 * IQR of the box, so they must range from 2 to 15.
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answer these questions
1. 3 1/2 + 3/4 =
2. 5/6 0f 54 =
put both answers
Look at the attached picture...
Hope it will help you....
Emma received grades of 68, 74, and 86 on 3 tests. What is the lowest grade she could get on a 4th test if she needs her average to be 80 or higher?
Answer:
92
Step-by-step explanation:
68+74+86+x/4 ≤ 80
HELP !!!!!!!!!!!!!!!!!!!!!!!!! i just to lazy
Answer:
34
Step-by-step explanation:
you multiply 4 times 8 and 1.5 times 4 and 1.5 times 2
Write the slope-intercept form of an equation that passes through the points (3,7) and (5,11)
Simplify the expressions:
1) [tex]\sqrt{x^6}[/tex] where x<0
2) [tex]\sqrt{m^4}[/tex]
3) 1.5 * [tex]\sqrt{t^1 ^4}[/tex] where t<0
Answer:
1. -x³
2. m²
3. -1.5t⁷
Step-by-step explanation:
x⁶^½ = +/- x³
Since x is negative, postive square root would be -x³
m⁴^½ = +/- m²
Positive square root is m²
t¹⁷^½ = +/- t⁷
Since t is negative, postive square root would be -t⁷
1.5 × -t⁷ = -1.5t⁷
can someone please help with this ?
Answer:
Step-by-step explanation:
If we are to find f(x) + g(x) that we means that we are to add the functions together by combining like terms, if any, and put it all together into one function. Adding them looks like this:
[tex]-3x+7+2x^2-8[/tex] and combining like terms gives us
[tex]2x^2-3x-1[/tex]
